Observations and analysis of early-type stars at infrared wavelengths - Chapter 2 The HI infrared line spectrum for Be stars with low-density discs.

UvA-DARE is a service provided by the library of the University of Amsterdam (https://dare.uva.nl)

Observations and analysis of early-type stars at infrared wavelengths

Zaal, P.A.

Publication date

2000

Link to publication

Citation for published version (APA):

Zaal, P. A. (2000). Observations and analysis of early-type stars at infrared wavelengths.

General rights

It is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s)

and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open

content license (like Creative Commons).

Disclaimer/Complaints regulations

If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please

let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material

inaccessible and/or remove it from the website. Please Ask the Library: https://uba.uva.nl/en/contact, or a letter

to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You

will be contacted as soon as possible.

Chapterr 2

Thee HI infrared line spectrum for Be

starss with low-density discs.

P.A.. Zaal, L.B.F.M. Waters, J.M. Marlborough

A&AA&A 299, 574 (1995)

Wee present theoretical Ha and HI infrared recombination line calculations for

low-densityy discs around B stars. Such a disc shows no visible emission in

Ha,, while the HI IR recombination lines are in emission. This phenomenon

hass been found in the spectrum of the B0.2V star, r Sco and could be

sim-ulatedd with a simple disc model. As an extension of that particular case we

calculatee the entire IR HI line spectrum of a normal B star surrounded by

aa low-density disc with a theoretical curve of growth for HI IR line fluxes,

whichh we introduce as a tool for studying low-density discs. We find that

IRR emission lines may be detectable for densities up to about 10

-14

gem

-3

,

whichh is a factor 10

2

— 10

3

lower than typically found in Be stars. For

dif-ferentt spectral types, BO, B2, B5 and B8 we determined the density range for

whichh emission is prominent in the IR recombination lines but not in Ha.

2.11 Introduction

Recently,, high resolution IR spectra of the B0.2V star T Sco revealed the presence of

surprisinglyy strong Bra and Br7 line emission (Waters et al, 1993, hereafter referred to

ass Paper I). This was unexpected because the Balmer lines for r Sco are in absorption.

However,, perhaps in hindsight this result should not have been as unexpected for two

reasons.. First, Smith and Karp (1978, 1979) noted that all photospheric absorption lines

theyy observed in r Sco in the optical and ultraviolet wavelength regions showed slightly

depressed,, short wavelength wings, suggesting to them some kind of macroscopic

mo-tionss even in the deep layers of the photosphere. Second, Furenlid and Young (1980)

observedd 60 main sequence B stars of types BO - B3 and found the Ho absorption line inn many of these to be asymmetric with a depressed short wavelength wing. The degree off asymmetry was correlated with v-sini. The observations of r Sco were interpreted in termss of a two-component stellar wind model, which is similar to the model widely used too explain the observations of the classical Be stars. This model consists of a high-density, low-velocity,, rotating and slowly expanding disc in the equatorial plane of a (rapidly ro-tating)) star, and a low-density, high-velocity wind at higher latitudes. The high density componentt produces the Ha line emission and IR free-free and free-bound continuum emission,, while the fast UV wind can be seen in absorption in UV resonance lines of ions off trace elements such as C IV and Si IV.

Thee Ha, Bra and Br7 line profiles of r Sco could be closely approximated with a simple discc model (paper I), which only includes the disc component. The wind observed in the highh excitation UV resonance lines has far too low a density to produce the observed IR lines.. The Bra line flux gives a value for the Emission Measure, log EM = 57.1 c m- 3 (paperr I). This is much higher than the EM derived from the UV resonance lines and from thee X-ray emission, but can be explained with a disc at a density which is a factor 100 lowerr than typically found in Be stars. The interpretation of the line emission in r Sco in termss of a circumstellar disc is not unique however. Other geometries may also be capable off reproducing the observed line profiles. In addition, non-LTE effects in the outer atmo-spheree of OB stars may result in an increase of the source function near the line center for thee high-level a transitions of Hydrogen (Murdoch et al., 1994), thus producing a narrow emissionn peak near the line center. Murdoch et al. use this model to explain the Bra (and Br7)) emission seen in the 09V star 10 Lac.

Thee observations of r Sco demonstrate the probability of having strong IR HI emission liness without noticeable emission in the photospheric Ha absorption line, while the latter hass a much larger transition probability than the IR HI lines. This strange effect can occur ass a result of the steep underlying continuum, which for hot stars closely resembles the tail off a hot black body. In the optical, the (intrinsically strong) Ha line emission competes withh a strong continuum, but in the IR the continuum is much weaker and so (weak) IR HII recombination lines can be observed in emission. This implies that a class of hot stars mayy exist whose optical spectra are normal but whose IR spectra show emission lines. Byy introducing a curve of growth for HI IR line fluxes we will study the HI IR spec-trumm and will test the disc model by making a case B approximation for HI IR line fluxes (sectionn 2.2.1-2.2.3). Following from paper I we will use r Sco as an example for demon-stratingg the implications of the curve of growth (section 2.2.4). For r Sco this method appearss to be a good tool to study the disc properties, and in the near future its capability willl be improved in order to study Be stars more generally. In the last part (section 2.3) wee will study the optical Ha line profile and the HI IR line profiles for other B types, in orderr to adopt a disc density range, where we expect to detect HI IR line emission while thee optical Ha line profile hardly shows emission.

2.22.2 The HI line calculations 21 1

2.22 The HI line calculations

Inn this section we will study the HI IR line spectrum for a BO star surrounded by a disc whichh shows emission in the IR HI lines without detectable emission in the optical Ha photosphericc absorption line. This restricts the density in the disc to a value a factor 102 -- 103 lower than found for normal Be stars. We calculated several HI IR line profiles in thee range between 2 ^m and 60 /im with a simple disc model (section 2.2.2), which takes intoo account the line optical depth and the bound-free and free-free contributions from thee disc to the continuum. To obtain better insight into the line optical depth, we will go throughh the definition for the line absorption coefficient.

2.2.11 The line optical depth

Thee quantum mechanical absorption coefficient per unit length, av for the self absorption

off line radiation resulting from a transition from an upper energy level m to a lower level nn (Lang, 1974) is

cc

22

NN

nn

gg

mm A

(

l

_9

J

J?A

(j}mn{u) ( 2 1 )

8TTT u2gnnl \ gmNni

wheree JV„ is the population of level n, Amn is the Einstein coefficient for a spontaneous

transitionn from an upper level m to a lower level n, n„ is the index of refraction of the medium,, which is close to 1, gn is the statistical weight (for hydrogen gm = 2 ^ ) and

4>mn{v)4>mn{v) is the line profile function.

Fromm the Saha-Boltzmann equation we can express Nn as,

NN

"" = ^ZkTrn-'"-

N

'

N

--^

vtT (2

-

2)

wheree k is the Boltzmann constant, T the temperature, me the electron mass, N{ and Ne

thee number density for the ions and electrons, Xi is the ionization energy and Xn the exci-tationn energy of the lower level n.

Iff we assume local thermodynamic equilibrium (LTE), we obtain from Boltzmann's equa-tion, ,

(2.3) )

ffn^mffn^m _ -hv/kT

ggmmNNn n

Thee line profile, 4>mn(v) is assumed to be a Gaussian profile

* „ > ) == * ? (2.4)

y/lTVTy/lTVT v

withh V = Vb + c (J/ - v0)ju where V0 is the radial velocity (projected along the line of

totall microscopic velocity, Vj is defined as

(

'2kT'2kT \2

—— + V?\ w 2 0 k m s -1 _{for a BO star (2.5)}

m00 J

wheree T is the disc temperature, m0 the atomic mass and Vt is the turbulent velocity of the

disc.. If we substitute in equations 2.2, 2.3 and 2.4 into equation (1) we obtain au under

LTEE conditions,

ll

NN

ll

N,(^y(l-e-N,(^y(l-e-

hh

^^

kTkT

)A)A

mn mn

l6nl6n33VVTT{2m{2meekT)VkT)V22' '

.. n^e(*-x«)/*T.e-(v-Vi)Vv» (26)

Thiss equation shows that the absorption coefficient depends not only on wavelength and

AAmnmn,, but also on \n and nm of the specific line intensity, and it depends on the velocity

fieldfield and temperature as well.

2.2.22 The curve of growth

Wee will present a theoretical curve of growth (COG) for HI line fluxes in the infrared. Lamerss & Waters (1984) already developed a COG for Be stars where they plotted the IRR continuum excess flux from the disc against an optical depth parameter to study the densityy and its gradient within the disc. We define a line optical depth parameter from sectionn 2.2.1 and develop a COG for HI IR line fluxes in a similar way as done by Lamers && Waters.

Thee line optical depth parameter, £ jm e

Thee line optical depth (from Eq. 2.6) is defined in such a way that it is separated in aa line dependent term, a term dependent on the stellar and disc parameters and a term dependentt on the line of sight. The first two terms, which include all terms except the geometricc dependencies, give a general expression for the line optical depth parameter

EElineline (seeEq. 2 . 9 - 2 . 1 2 ) .

Fromm the absorption coefficient we get an expression for the line optical depth along a linee of sight through the disc

/

oo o

ct{i/)dzct{i/)dz (2.7)

-oo o

wheree a(u) is as defined in Eq. 2.6. In order to work out the integral we adopt a coordinate systemm as shown in figure 2.1, where P is the impact parameter.

2.22.2 The HI line calculations 23 3

TOO OBSERVER

Figuree 2.1. The adopted coordinate system.

N,{r)NN,{r)Ncc{r){r) = ~/N?{r" IJ,IJ,22_mm22 H H

p\r) p\r)

pfo pfo

-20 -20 (2.8) ) wheree 7 is the ionization fraction (Ni/Ne), fj, the mean molecular weight of the ions and mumu the mass of hydrogen. If we combine Eq. 2.6, 2.7 and 2.8 we obtain

r„(V,p,r)r„(V,p,r) = E,

meme I ,,X2 X2

-2/3+1 1

V ^ ^ _{P' P'} ee

-iy-v-iy-v

00

wr/v}wr/v}

dx dx

(2.9) )

wheree we made a coordinate transformation for z; z2 = r2 - p2, and defined x = r/R* (similarr to Wright and Barlow, 1975). The line optical depth parameter Eune is defined as

ElineEline — ^line ' sigtar wheree X{ine is defined as

andd Xstar is defined as

(1 1 „-hv/kT} „-hv/kT} XXstarstar = 6.23 107

pllK pllK

(2.10) ) (2.11) ) (2.12) ) fj,Wfj,WTTTT33//2 2

wheree Xnne depends on the specific line transition (the T dependence for Xune is very weak)) and Xstar depends on the temperature and the turbulent velocity in the disc. For Eq.. 2.11 and Eq. 2.12 cgs units have been used, and K is the stellar radius in Re. The dependenciess on the line of sight are now included in the integral over the line of sight, Eq. 2.9.. This notation is the same used by Poeckert & Marlborough (1978) and is formulated

inn the same way as done by Lamers & Waters (1984) for calculating the continuum excess fromm the disc.

Thee boundary conditions depend on the geometry: a spherically symmetric shell or a discc like structure. The latter introduces limitations for x and p which depend on the inclinationn angle and the opening angle of the disc. If we integrate over the line of sight, wee get

UV,p,<f>)=UV,p,<f>)= f ™ " Sye-W^dt (2.13)

Jo Jo

wheree S„ is the source function which we assume to be constant over the line profile and equall to the Planck function, B,,. For the the total flux we get

F„{V)F„{V) = I" r I

u

{V,p,<f>)pdpd<f> (2.14)

JOJO J-K

Thee numerical HI IR line flux calculations

AA parameter study, varying the density and its gradient, gives a better physical insight in thee disc properties. This was done by calculating the HI IR line fluxes with the help of a simplee disc model (Waters 1986).

Thee disc model consists of a disc with an opening angle 0, with 6 = 5°, and a density distribution,, p{r) = p0(r j R+Y0, where /? is the logarithmic density gradient. For mass

continuityy this corresponds to a velocity v(r) = vo{r/Ri,Y~2. We adopt Keplerian

ro-tation,, v^{r) = v^flJR+jr, for the disc where t^i0 is 0.7 times i v the breakup velocity,

whichh is about 690 k m s- 1 for a BO star. The disc is assumed to be isothermal at a temper-aturee of 0.6Tefj (see e.g. Waters & Marlborough, 1992) and has an outer radius (Rdisc)

off 16 /?*. Beyond this radius the disc density is assumed to be negligible low.

Thee IR lines were calculated from the Saha-Boltzmann equation using the local values of

NNee and Te, while the Ho line profiles were calculated by solving thee equations of statistical

equilibriumm for the levels 1 to 4 for a gas consisting of pure H (Poeckert & Marlborough, 1978),, taking into account the underlying photospheric absorption line (Kurucz, 1979). In thesee calculations the disc is assumed to contain pure H. The line profiles were calculated usingg a ray-tracing technique, where for each line profile several hundred lines of sight weree used.

Thee curve of growth

Inn the theoretical COG (see Fig. 2.2) we plotted the HI IR line flux divided by the wave-lengthh on the vertical axis and the optical depth parameter (from Eq. 2.10) on the horizon-tall axis. The IR HI line fluxes were calculated for a BO star surrounded by a low-density discc seen pole-on. The stellar and disc parameters used in the disc model are as given inn Table 2.2 (Section 2.3). Only HI IR lines within the wavelength range between 2 pm

2.22.2 The HI line calculations 25 5 r< r< M M O O oo # oo * ' 00 1 2 logg (Ellne)

Figuree 2.2. COG for HI IR lines from a BO star surrounded by a low-density disc seen pole-on.

Thee HI IR line fluxes, between 2 fim and 60 /im, are calculated with a disc model for 3 radial densityy gradients, the upper curve for /? = 2, the middle for (3 = 2.5 and the lower for /3 = 3. andd 60 ^m were considered and are expressed in terms of the photospheric flux, i.e. the equivalentt width (EW). We used the following values for the density and its logarithmic gradient;; p0 : == 4, 2, 1, 0.5 -10"

13

gem- 3 and 0 = 2, 2.5 and 3. The density range is chosen inn such a way that the HI IR line fluxes remains detectable while the Ha line emission iss clearly visible at the higher densities and is hardly visible at the lower densities. The electronn density, Ne follows from

NNee(r)(r) = -yNi{r) 7PQ) )

y,my,mH H

(2.15) ) wheree in this case the ionization fraction, 7 is 1 and the mean molecular weight for ions,

HH is 1 (i.e. the gas consists of pure H in the disc model).

Fig.. 2.2 shows three curves, each curve represents several IR line fluxes calculated for thee different densities and for one density gradient. We point out that Xune is proportional

too A (see Eq. 2.11 where An>n is proportional to A- 1) i.e. lines in the far-IR may become

opticallyy thick despite a decrease in the Einstein A coefficient towards higher n transi-tions. .

Forr low values for the optical depth parameter Eiine the HI IR lines are optically thin;

(EW/A)) oc EM and the slope of the curve shows no dependence on the value of f3. In the opticallyy thin region the steep gradient only affects the overall line flux; a steep density gradient,, (3 implies a low EM, so a lower line flux. A quantitative description for the EM inn case B will be given in section 2.2.3.

Forr higher values for Eiine the IR HI lines become optically thick (for the larger densities

rruu % 1), the curve no longer shows a linear increase in line flux as Eline increases and

thee slope of the curve now becomes dependent on (3. So the shape of the curve may give informationn on the density gradient in the disc. For a disc with a shallow density gradient thee lines are formed in a relative large, low-density region while in the case of a steep densityy gradient the lines are formed in a smaller and denser region where the lines are opticallyy thicker. So a steep radial density gradient yields a flatter curve in the optically thickk part. The onset of the optically thick part also depends on the gradient within the disc,, but this effect is weak.

Thee COG for line fluxes has some useful applications: with IR HI line observations, one mayy plot \og(Xline) instead of log( £/,-„<.) on the horizontal axis; comparison with the

the-oreticall curve will then give information about Xstar, thus about the density within the

disc.. By selecting some HI IR lines which are on the optically thick part of the curve (like thee HI 10-9 line at 38.8 //m) and some optically thin lines (like the HI 11-8 at 12.3 ^m), onee can make an estimate for the density (from the horizontal shift). Finally the shape of thee curve may give an estimate for the radial density gradient within the disc.

2.2.33 The simple approximation

Wee now compare the numerical calculations to optically thin calculations using case B recombinationn theory, i.e. optically thick in the Lyman lines and optically thin in all other lines.. This is done to facilitate the calculations in the low-density limit, and to verify the accuracyy of the numerical code.

Ann expression for the emissivity, j„im is given by Brocklehurst (1971)

47rjm,nn = hum}nNeN,am^n(Te) (2.16)

wheree vm<n is the line frequency, h the Planck's constant, Ne and iV,- are the local

elec-tronn and the local ion density, and am_+n(Te) is the effective recombination rate. For the

aamm^^nn(T(Tee)) we use the case B values from Hummer and Storey (1987). The recombination

coefficientt includes the dominant physical processes like radiative recombination, radia-tivee cascade, collisional redistribution of energy by electrons and collisional redistribution off angular momentum by ions.

2.22.2 The UI line calculations 27 7

Thee disc is at constant temperature of 0.6Teff, has an opening angle 0, and a radial

den-sityy distribution, p(r) = po(r/R^)~p_{. Integrating Eq. 2.16 over the volume of the disc}

gives s

huhuminminggmm^^nnEM(NEM(N<!<!)) _. hpprhppr

~ 4 ^ ( }

wheree Iappr is the approximate total line emission, D is the stellar distance and EM is the e

volumee emission measure. If we calculate the EM for a disc (as described) which extends too a radius, Rdisa we get

EMEM = 4 p ^ -Rl-pl- (*<%*" l)) sin 9 ( n / 1 . 5 ) (2.18) wheree 7 is the ionization fraction, p. the mean molecular weight for ions, mH is the mass

off a hydrogen atom, p0 the density at r = R*, 6 the opening angle and Rdi3C is the radius

off the disc in units of fl*. We may use Eq. 2.18 if we assume that the disc is optically thin andd that there is no occultation (i.e. a pole-on orientation). If we see the disc edge-on, a largee part of the disc will be obscured by the star resulting in a lower EM(iVe), a factor 2

lowerr than for a pole-on view. In the edge-on case this results in a lower integrated line flux. .

Thee COG with the approximate HI IR line fluxes

Fromm Eq. 2.17 we can calculate the case B line fluxes, which can be compared with our numericall results by making a COG for both methods as shown in Fig 2.3. Since we use ann (almost) pole-on orientation, the occultation of the disc material by the stellar photo-spheree is negligible and we may use Eq. 2.18 as an accurate expression for the emission measure.. For comparison we only used the fluxes calculated for a radial density gradient, /?? of 2.5 and an inclination angle of 5°.

Forr the case B line flux calculations (Eq. 2.17) we use the same stellar and disc parameters ass used in the disc model; for the effective recombination coefficient, a(ne,Te) we use

valuesvalues from Hummer & Storey (1987) for a disc temperature (Tj) as given in Table 2.2 (sectionn 2.3) and for an electron density of 108 cm- 3. The effective recombination coef-ficientficient is given for a gas which consists of a mixture of He and H with a mean molecular weightt for ions, p = 1.25. In order to calculate the HI IR line fluxes for the same electron densitiess as used for the in the disc model, we use Eq. 2.15 with; 7 — 1 and p equal too 1.25 (for a gas which consist of mixture of Hydrogen and Helium, N(He)/N(H) = 0.1) andd the disc densities, p(r) were chosen in such a way that the electron density equals the valuee as used in the disc model.

Thee numerical and approximate HI IR line fluxes for a density gradient 0 of 2.5 are plot-tedd in Fig. 2.3. The case B line fluxes are expressed in terms of the photospheric flux

- 1 00 1 2 logg (Eline)

Figuree 2.3. The COG for a BO star surrounded by a low-density disc seen pole-on, where the HI

IRR line fluxes are calculated numerically, with the disc model (filled in dots), and with the case B approximationn (open dots) at a density gradient (3 of 2.5.

(EW),, by using the Kurucz fluxes (1979) for the photospheric continuum. The HI IR fluxesfluxes calculated with the disc model are those from section 2.2.3.

Fromm this comparison we may conclude that for a small line optical depth, Etinc the

ana-lyticall calculations predict slightly smaller line fluxes. This offset between the two which mightt be due to the fact that the line calculations done numerically used level populations givenn by the combined Saha-Boltzmann equation, whereas the approximate line fluxes aree calculated with an effective recombination rate (Hummer & Storey, 1987) which in-cludess departure coefficients which still plays a role at these densities. The scatter in the analyticall curve is also due to this fact. A more quantitative statement will be made in sectionn 2.3.2. Furthermore one clearly sees that for larger values for EHne the HI IR lines

gett optically thick, at this point the analytical optically thin calculations overestimates the linee flux, as expected.

2.22.2 The HI line calculations

2.2.44 An example; A full HI IR spectrum for r Sco, a BO star

sur-roundedd by a low-density disc

Inn paper I we showed an example of a B0.2V star, r Scorpii, which showed emission in thee IR HI lines, Bra and Br7 without noticeable emission in Ho. The infrared HI recom-binationn lines for r Sco were obtained at UKIRT on July 28 and 29, 1992 (UT), using the echellee facility grating spectrometer, CGS4. The Ho line profile was obtained at the 1.4m Coudéé Auxiliary Telescope at ESO, La Silla on August 29, 1990. New observations in Julyy of 1993 for the HQ line (Oudmaijer, private communication) and for Bra show that theree still is emission in the IR HI line, Bra at 4.05 y.m without noticeable emission in Ha,, based on the observations which were almost simultaneous (1.5 month in between thee observations). - 4 4 M M I I N N - 5

6 6

o o M M M M S-. . 11 1 " "" - 6 x x 3 3 O O - 7 7 0.55 1 1.5 2 logg X {fim)

Figuree 2.4. The predicted spectrum (from the COG) for r Sco surrounded by a low density

discc seen pole-on (FWHM 68 kms"1). The density in the disc, p0 is 2 -1CT13 g cm"3 which we

Thee COG can be used as a tool to estimate XsiaT (Eq. 2.12) and thus give information

aboutt the density structure in the disc. The observations give the relation between the line fluxesfluxes and Xstar, while the theory gives the relation between the line fluxes and Eltne.

Comparisonn of the shape of the observed and theoretical curves yields information on the densityy structure of the disc, i.e. the density gradient ƒ?, while the horizontal shift, needed too fit the theory with the observations, yields the parameter X3tar, from which the density

poo can be derived if the stellar parameters are known.

Too make an estimate of the disc density and its gradient for r Sco we use the observed line fluxes,, Bra and B H (from paper I). The observed Br7 line flux was corrected in paper I forr the underlying photospheric line flux, which resulted in an increase of the line flux by aa factor of 2. New observations for B n (Murdoch et al., 1994) justify this correction by showingg that our suspected presence of the underlying absorption feature was right. These observedd line fluxes were plotted against Xline. Because we have only two observed line

fluxesfluxes for r Sco we can not say anything about the shape of the curve and thus about the densityy gradient. 0. The adopted values, from the horizontal shift, for p0 are 1.5, 2.1 and

3.0-- 10"13 gem- 3 if we assume a /? of respectively 2, 2.5 and 3. To make a quantitative statementt about the density gradient one needs to observe more line fluxes over a large as possiblee range for Xune.

Anotherr application of the COG for HI IR lines is that we can predict the full HI IR spec-trumm of T Sco. In Fig. 2.4 we plotted all line transitions between 2 fim and 60 ^m, up too the upper quantum level, m = 15. The predicted IR HI line fluxes were calculated by makingg a linear fit to the optically thin part and the optically thick part of the COG. We usee the COG as given in Fig. 2.2 where the HI IR line fluxes were calculated numerically withh a radial density gradient, (3 of 2.5 and the disc has an an inclination angle of 5°. For rr Sco we assume a density within the disc, p0 of 2 -10- 1 3 gem- 3, which follows from the

COGG adopted disc density. Note that for such a disc density Ha hardly shows emission (paperr I). The HI IR spectrum (Fig. 2.4) is adopted by assuming a single-peaked, Gaussian linee profile (pole-on orientation), with a FWHM of 68 kms- 1 (paper I). The underlying photospheree (Kurucz, 1979) is corrected for the bound-free and free-free contributions fromm the disc. At about 50 ^m the bound-free and free-free continuum excess flux from thee disc becomes apparent. In Table 2.1 we give for the 17 most prominent HI IR lines the wavelength,, the equivalent width, the integrated line flux and line over continuum ratio. Tablee 2.1 shows that for new observations one can use different HI IR lines as probes for low-densityy discs. The most prominent lines are HI 10-09 at 38.8 //m and the HI 11-10 at 52.55 fjm. Other HI line transitions at longer wavelengths will hardly show larger line over continuumm ratios, because the line optical depth, E,tne and the continuum excess flux,

Z„-ll are both linear with wavelength. The line flux will decrease for transitions at longer wavelengths;; this gives an optimum line to continuum ratio for the HI IR line transitions inn the mid-infrared.

2.32.3 A study ofB stars surrounded by a low-density disc 31 1

Tablee 2.1. The most prominent HI IR lines from Fig. 2.4, approximate for r Sco (FWHM of 68 kms-1_{).. IunJhont is the peak value of the linee relative to the total continuum in case of infinite}

spectrall resolution. line e 15-12 2 14-11 1 14-12 2 13-10 0 13-11 1 12-10 0 11-09 9 11-10 0 10-08 8 10-09 9 09-07 7 09-08 8 08-06 6 08-07 7 07-06 6 06-05 5 05-04 4 AA [/jm] 36.5 5 28.8 8 49.5 5 22.3 3 38.8 8 29.8 8 22.3 3 52.5 5 16.2 2 38.9 9 11.3 3 27.8 8 7.5 5 19.1 1 12.4 4 7.5 5 4.1 1 EW[A] ] 80.9 9 53.4 4 197.9 9 33.5 5 144.3 3 99.7 7 65.0 0 496.6 6 39.9 9 338.3 3 20.8 8 212.1 1 9.6 6 121.7 7 63.3 3 29.4 4 10.4 4 fi,„fi,„ee[Wm-[Wm-22l l 1.3955 10"18 2.2633 10~18 1.0955 10"18 3.8322 10"18 1.9600 10"18 3.6999 10"18 7.4366 10"18 2.2122 10~18 1.6166 10"17 4.5844 10-18 3.5322 10"17 1.0344 10"17 8.4299 10~17 2.5966 10"17 7.5100 10"17 2.6300 10~16 1.0600 10"15 11 line' * cont 1.92 2 1.77 7 2.66 6 1.62 2 2.54 4 2.38 8 2.21 1 4.92 2 2.02 2 4.61 1 1.76 6 4.16 6 1.53 3 3.64 4 3.12 2 2.63 3 2.06 6

2.33 A study of B stars surrounded by a low-density disc

Inn this section we make an estimation of the density range for our low-density discs. This rangee is characterized by HI IR lines in emission while the Balmer lines do not show anyy emission feature because of the strong underlying continuum. Also we like to get ann impression of how this range varies with spectral type: which normal B star has the largestt probability of being surrounded by a low-density disc, the early or late B types? Thee visibility of the line emission from the disc strongly depends on the orientation angle off the disc. Thus the orientation angle will also have a large impact on the density range forr the low-density discs. Changing the orientation from a pole-on to an edge-on view willl result in a shift upwards in this density range, i.e. low-density edge-on discs will be harderr to detect. We will derive the density range for the pole-on case by studying the Ha linee profile with the disc model and using the case B approximation for determining the HII IR line profiles.

2.3.11 The HQ and IR line profile calculations with the disc model.

Wee discriminate a normal Be star from a B star surrounded by a low-density disc using thee rate of distortion in the photospheric HQ absorption line profile. This distortion (disc emission)) depends on the density of the disc, p0, and the inclination angle, i, of the star.

Thesee density and inclination (i = 5°, 30°, 90D) dependencies are shown in Fig. 2.5 for aa BO star calculated with the disc model. The stellar parameters we used are given in Tablee 2.2. 1.4 4 1.2 2 1 1 0.8 8 0.6 6 1.4 4 ^^ 1.2 1 1 0.8 8 0.6 6 1.4 4 1.2 2 0.8 8 0.6 6 M i l l l

rhoo 2

ll l l I l

rhoo 1

II . . . . i l l l i i M l l _{I I II I I M l} 1.4 4 1.2 2 1 1 0.8 8 0.6 6 1.4 4 1.2 2 1 1 0.8 8 0.6 6 1.4 4 1.2 2 1 1 0.8 8 0.6 6 -500 0 5000 -500 0 500

Velocityy ( k m / s )

-500 0 500 0

Figuree 2.5. Ho disc model calculations for a B0 star at a inclination angle of 5°, 30° and 90°

forr 3 different densities, p0, the upper, middle and lower panel are at a density, p0 of resp. 4, 2, 1

2.32.3 A study ofB stars surrounded by a low-density disc 33 3

Thee inclination angle has a large effect upon the visibility of the Ha emission from the disc;; when the inclination angle is changed from pole-on to edge-on all the emission fromm the disc is spread out over a larger velocity range. Thus, for the edge-on case the photosphericc absorption profile will hardly be distorted by the line emission from the disc. Fromm the rate of distortion in photospheric line profile of Ha one might roughly define ann upper limit for the disc density. Our class of low-density discs exists up to this critical densityy at which the emission from the disc becomes clearly visible in the line profile of Ha.. The difficulty in this case is the not well determined intrinsic photospheric absorption linee profile of Ha. Often one notices the distortion in Ha after finding possible disc featuress in the infrared.

Inn the same way as done for a BO star surrounded by a disc, the Ha line profiles were calculatedd for stars with spectral type B2, B5 and B8. In all these cases we studied the Ha profilee for three inclination angles, i= 5°, 30° and 90°. For the underlying photospheric continuumm (Kurucz, 1979) we used values for #*, M* and Teff as given in Table 2.2. The

temperaturee of the disc we used is 0.6TeJf. From these calculations we determined how

thee distortion from the disc in the photospheric Ha line profile depends on spectral type (shownn in Fig. 2.7). A discussion on the derived critical density and the dependence on inclinationn angle is given in section 2.3.3.

Thee disc density and inclination dependencies on the numerical HI IR line profiles are shownn in Fig. 2.6. Note that these profiles are calculated, under the same conditions as donee for the Ha line profiles in Fig. 2.5. Also for the Ffl IR lines the inclination has a large impactt on the line profiles; an edge-on orientation will decrease the line over continuum ratioo and so the HI IR line will be harder to detect than for a pole-on orientation. The advantagee for HI IR lines is the flat underlying continuum which makes it easier to detect thee emission from the disc.

Tablee 2.2. The stellar parameters for the different spectral types.

spectrall type BO O B2 2 B5 5 B8 8 M*M* (M0) 15 5 9.0 0 4.5 5 3.0 0 R*R* (R@) 6.0 0 4.3 3 3.0 0 2.5 5 TTeffeff (K) 30000 0 23000 0 15000 0 12000 0

2.3.22 The approximate HI IR line fluxes in the low-density limit.

Forr determination of the lower limit for our low-density discs the following question needs too be answered: which HI IR line has the most prominent line over continuum ratio and at

3 3 2.5 5 2 2 11 5 3 3 2.5 5 2 2 1.5 5 1 1 3 3 2.5 5 2 2 1.5 5 1 1 -' ' r r r r r r ^ ^ : : --r --r r r +--i +--i I1 1 1 1 r h oo 4

_J J

r h oo 2

i i

11 1 1 1 r h oo 1 || , i , i | , , _ | 11 = 5" :

i i

I I

11 i

M i l ; ; _J"V V ii 1 i i i i ii i i i 1 i i -. . -'' ' + + ^ ^ - ii i i ii i i i I ii = / ^ \ \ ^~~—^~~—v_ v_ III II 1 II 11 1 1 1 1 1 1 1 11 1 30° ° ,, 1 11 1

+f< <

i i - f f i --jj i | i i i 11 1 | I I I - ii i 1 i i i 11 i i i i 1 i ,_ ll = 90° -: -= = -_ -_ _; ; : : -_ -_ -_ -_ -_ -_ _ _ ii | i i i i | i r -_ -_ ---_ ---_ Z Z , l , , i , l , , ---500 0 _{5000 -500 0 500} Velocityy ( k m / s ) -500 0 500 0 3 3 2.5 5 2 2 1.5 5 1 1 3 3 2.5 5 2 2 1.5 5 1 1 3 3 2.5 5 2 2 1.5 5 1 1

Figuree 2.6. Disc model calculations for a B0 star at a inclination angle of 5°, 30° and 90° for the

Braa line (4.05 (im) for 3 different densities, p0, the upper, middle and lower panel are at a density,

PoPo of resp. 4, 2, 1 -10-13 gem-3.

whichh disc density is this HI IR line still detectable? A quick estimate of the (peak) line too continuum ratio for each HI IR line can be made with the case B approximation for the HII IR line fluxes (section 2.2.3). In the low-density limit the optically thin approximation enabless us to simplify and speed up the HI IR line calculations. The justification of using thiss simple approximation follows from Fig. 2.3, where the approximation is compared withh the numerically calculated line fluxes. In the low-density limit (lower left corner of Fig.. 2.2) the approximate line fluxes fits the fluxes calculated numerically within a factor 0.99 - 0.6. The discrepancy between the two methods can be explained by the fact that the approximatedd fluxes where calculated with NLTE recombination coefficients, whereas the

2.32.3 A study ofB stars surrounded by a low-density disc 35 5

discc model assumes LTE. This results in a discrepancy which is the largest (about 40 %) forr the strongest line transitions. Whereas the weaker line transitions shows a discrepancy off only 10 %. Since in the low-density limit the discrepancy between the two methods onlyy gets smaller we will use this simple approximation for making an estimate of the HI IRR line fluxes.

Wee calculated all HI line transitions within a wavelength range (between 2/^m and 50^m) whichh is largely covered by the Short Wavelength Spectrometer (SWS) on board the In-fraredd Space Observatory ISO. The case B line fluxes used are derived from Eq. 2.17, withh the stellar parameters as given in Table 2.2, for all HI IR line transitions up to the upperr quantum level m = 15. In order to derive a line over continuum ratio, all the HI IR linee fluxes were fitted with a single (double) Gaussian line profile for pole-on (edge-on) orientation.. For the pole-on case we used a FWHM of 68 kms- 1 which was derived from thee observed line profiles for r Sco (paper I) and for the edge-on case we used a line pro-filefile derived from the numerical disc model calculations: a double Gaussian with a FWHM off 200 kms- 1 _{and a peak separation of 560 kms}- 1 _{(see Fig. 5.2). In these calculations for}

thee edge-on case we took into account the occultation effect which reduces the HI IR line fluxx by a factor 2 if we go from a pole-on to a edge-on orientation. For the underlying photosphericc continuum we adopted the values from Kurucz (1979) with /?*, M* and Tejj

ass given in Table 2.2.

Thee detection limit for the HI IR line fluxes (the density above which the strongest HI IR linee is still detectable) is found by recalculating the line to continuum ratio (for all HI IR lines)) while reducing the disc density iteratively until the detection limit is reached for the mostt apparent line. Here we defined a line over continuum ratio of 1.05 (peak value) as detectionn limit.

Fromm these calculations we find that, for every B spectral type (B0, B2, B5 and B8), the HII IR line, 10-09 at 38.8 (im has the largest line over continuum ratio in the mid-infrared (upp to 50 fim). This line, as well as the other lines in Table 2.1, will be good target lines forr ISO to detect with the SWS. Because the HI IR lines, like Bra and Br7 for r Sco are alreadyy found in emission, other lines in the mid-infrared must show much larger values forr IunJhont if our model is appropriate. In the case of a pole-on orientation this resulted inn a lower limit as shown in Fig. 2.7.

2.3.33 The density range for low-density discs

Thee density range for our class of low-density discs is given in Fig 2.7, where the lower limitt is calculated with the case B approximation and the upper limit is determined from thee rate of distortion in the Ha photospheric line profile calculated with the disc model. Thee range in disc density for our low-density discs decreases for later spectral types. This iss due to the following: for later spectral types we have an increase in the line strengths forr HI recombination lines, whereas the effective temperature decreases (the optical

con-A con-A

Normall Be s t a r s

Limitt due to emission in Ha

-BOO B2 , . B5 B8

spectraltype e

Figuree 2.7. The density range for p0 for our low-density discs where we see HI IR emission lines,

whilee in the optical HI lines, like Ha, shows no emission features. The lower limit, determined by thee detectability of the line (/(me//co„(.), is giver, for a pole-on view.

tinuumm decreases). So the same disc density will cause a greater distortion in the photo-sphericc absorption line of Ho for these later type stars.

Thee orientation of the disc has a large impact on both limits. In the edge-on case the line fluxflux smears out over a large frequency space and reduces the (peak) line over continuum ratioo for the HI IR lines. This causes an overall shift upwards by a factor of 4 in density forr the lower limit (if going from pole-on to a edge-on orientation). The upper limit will alsoo shift upwards although it is difficult to make a quantitative statement about the impact off the orientation on the distortion in the Ha line profile. From Fig. 2.5 the edge-on case showss no clear asymmetric features up to a p0 of 4 -10~13 gem- 3, so certainly more than

aa factor of 2. Thus, going from a pole-on to an edge-on view results in an overall upward shiftt of the density range for our B stars surrounded by low-density discs.

2.44 Discussion

Thee application of the COG on r Sco, considered as a Be star surrounded by a low-density discc with a pole-on orientation, may be seen as an example how effective this method is in gettingg a better insight in the line formation, the discs density and its structure. The COG forr HI IR line fluxes method may become as important as the COG for the continuum excesss (now the IR spectroscopy is going through fast improvements). Whether or not r Scoo has a disc like structure, this study on discs around B stars predicts how the HI IR

2.42.4 Discussion 37 7

spectrumm may look in the low-density limit. The HI IR line, 10-09 at 38.8 fim is the HI IRR line with the largest line over continuum ratio in the mid-infrared (up to 50 ^m). This line,, as well as the other lines in Table 2.1, will be good target lines to detect low-density discss with the SWS.

Thee inclination angle for the disc has a large impact on the (peak) line over continuum ratioratio for the HI IR line profiles and also on the rate of distortion in the photospheric Ha linee profile. Both, the occultation effect and the smearing out of the line flux over a larger frequencyy space play a role: if going from a pole-on to a edge-on orientation this results in aa shift upwards for the range in density for our low-density discs (with about a factor 4 in density).. From the investigated density space for the different spectral types we conclude thatt the normal early B type stars have the largest probability of being surrounded by a low-densityy disc which can only be traced by looking at the HI IR line transitions. Ass an extension one might study the impact of the inclination angle on the line optical depthh in the optically thick part of the COG for HI IR line fluxes. We expect that an edge-onn orientation will give a less steep gradient in the optically thick part of the COG thann in case of a pole-on orientation, i.e. the lines become optically thick, because of the linee of sight through the disc gets longer. On the other side, because of the larger velocity space,, line radiation might escape more easily.

Wee pointed out in paper I that in the case of r Sco the emission might come from a low-densityy disc seen pole-on, although other models could not be excluded. Murdoch et al. (1994)) have found also Bra and Bry in emission for r Sco and a for second star, 10 Lac (a 0 99 MK standard star). Murdoch et al. (1994) explained these emission features by using aa spherical NLTE atmospheric model. They suggest that a disc model with a pole-on ori-entationn is rather exceptional. New observations for r Sco for other HI IR line transitions mightt give information on which atmospheric model suits best: the disc model will give otherr line ratios than the NLTE model used by Murdoch et al. (1994). The disc model calculationss for B stars demonstrate that, under LTE-conditions, other HI IR lines show muchh stronger line to continuum ratios than the already observed Bra.

References s

Brocklehurstt M. 1971.MNRAS 153,471

Castorr J.I., Lamers H.J.G.L.M. 1979, Astrophys. J. Suppl. 39,481 Furentidd I., Young A. 1980, ApJ, 240, L59

Hummerr D.G., Storey P.J. 1987, MNRAS 224,801 Kuruczz R.L. 1979, ApJS, 40,1

Lamerss H.J.G.L.M., Waters L.B.F.M. 1984, Astron. Astrophys. 136, 37 Langg K.R. 1974, Astrophysical Formulae, p96

Poeckertt R., Marlborough J.M. 1978, ApJ 220,940 Smithh M.A., and Karp A.H. 1978, ApJ, 219, 522 Smithh M.A., and Karp A.H. 1979, ApJ, 230,156 Waterss L.B.F.M.: 1986, A&A 162,121

Waterss L.B.F.M., Marlborough J.M. 1992, A&A 256, 195